Do Fuses make a difference ib sound?

Hafler didn’t think so.  All of my Haflers have the output fused. Those has saved my butt while my head was up it.   The difference between with and without can’t be discerned.  Keep em. 

Can someone explain the mechanism(s) that create the differences that are attributed to different brands of fuses?

Expectation bias is a strong force...Bussman and Littelfuse products may be the only fuses you need, and serious equipment designers  like Nelson Pass agree. However, if you can imagine a magical property and apply it to an already working fuse design, and charge multiple times it's actual cost to make a pile of money for yourself, do it!  Some people will feel better about themselves by thinking it's money well spent and apply magical results in their little minds. Years ago I got a pile of Synergistic Research fuses from a friend and carefully tested 'em changing direction, etc., recorded the differences between them and standard fuses (of which there were none), and sent them back. Enough for me! 

Not sure. Bought used SR orange for all my components. They are very reasonably priced used, so a low cost tweak. As with other low cost tweaks, if they improve things… great… but don’t A/B. As @mitch2 said, they certainly don’t sound worse. 

Unwise to monkey with stock fuses as a layperson. Wyred4Sound offers fuse upgrades in their upgrade options on the STP SE. Connectors are cheaply built so multiple fuse r/r may loosen up the contacts. Or if you spend enough for nice boards with nice components the fuse will be selected by the engineers. Fuses are safety devices.